Project description
Probing the non-linear dynamics of large fermionic systems
Fermionic systems play a significant role in describing molecules and condensed matter. Their time evolution is determined by the Schrödinger equation which, however, is very challenging to analyse for large systems with many particles. Funded by the Marie Skłodowska-Curie Actions programme, the EFFECT project aims to enhance understanding of the non-equilibrium dynamics of large fermionic systems and their interaction with quantised electromagnetic fields. The project plans to develop new mathematical tools to approximate such large systems by simpler effective evolution equations for fermionic systems at zero and finite temperatures.
Objective
The goal of this project is to substantially improve the understanding of the non-equilibrium dynamics of large fermionic systems and their interaction with the quantized electromagnetic field. Fermionic systems play a significant role in the description of molecules and condensed matter. Their time evolution is determined by the Schrödinger equation which, however, is very challenging to analyze for large systems with many particles. For this reason simpler effective equations are used to approximately predict the time evolution. These are easier to investigate but less exact. In physics, effective equations are derived by heuristic arguments. Beyond that, a mathematical analysis is essential to prove the range of validity of the applied approximation. In the scope of this project new mathematical tools will be developed to rigorously derive effective evolution equations for fermionic systems at zero and finite temperature. The Hartree-Fock equation with Coulomb potential will be derived from the Schrödinger equation in a many-fermion mean-field limit which is coupled to a semiclassical limit. In the same scaling limit the use of the (fermionic) Maxwell-Schrödinger equations as approximate time evolution of the Pauli-Fierz Hamiltonian will be justified. Moreover, it will be proven that the quantum fluctuations around the effective equations are described by Bogoliubov theory. Explicit estimates for the error caused by the approximation will be provided. In total, this will enhance the understanding about the creation of correlations among fermions and the emergence of classical field theories from quantum field theories. The derivations are long outstanding and there is an extensive need for new mathematical methods in semiclassical analysis and many-body quantum mechanics. It is expected that the new techniques will also have a strong impact on studies about dilute Bose gases at positive temperature and fermionic systems in the kinetic regime.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences physical sciences electromagnetism and electronics electromagnetism
- natural sciences physical sciences theoretical physics particle physics fermions
- natural sciences mathematics pure mathematics mathematical analysis
- natural sciences physical sciences quantum physics quantum field theory
- natural sciences computer and information sciences artificial intelligence heuristic programming
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions
MAIN PROGRAMME
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H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) H2020-MSCA-IF-2020
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
4051 Basel
Switzerland
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.